CN117675110A - Sparse Bayesian signal reconstruction method based on multiple measurement vector model - Google Patents

Abstract

The invention discloses a sparse Bayesian signal reconstruction method based on a multiple measurement vector model, which includes the following steps: Step S1: given base station received signal, equivalent channel matrix, number of devices and spread spectrum gain, combined with automatic decision-making technology Assign structured prior Gaussian information to the transmitted signal, assign ordinary Gaussian prior information to the noise signal, and initialize the hyperparameter set; Step S2: Use Bayes’ theorem to calculate the posterior distribution of the transmitted signal; Step S3: Expect the maximum through iteration method to update the hyperparameter set; Step S4: Determine whether the iteration termination condition is met. If it is met, exit the loop and output the restored emission signal. If it is not met, return to step S2 for the next round of iteration. The present invention uses the internal structure of user information to decompose multi-user detection under multi-time slots into multiple single time slots, and then operates each stage to extract user information to avoid multi-user detection being limited by time slots.

Description

A sparse Bayesian signal reconstruction method based on multiple measurement vector models

Technical field

The invention relates to a multi-user detection method for an authorization-free non-orthogonal multiple access system, and in particular, to a sparse Bayesian signal reconstruction method based on a multiple measurement vector model.

Background technique

In future wireless communications, massive machine type communication (mMTC) plays a key role. It can be applied to fields such as smart cities, smart homes, energy management, and health care, and supports large-scale devices to connect to base stations (BS). However, mMTC devices are usually activated only when needed, which is very different from human-centric communication. And traditional human-oriented communication systems are difficult to meet the massive connection needs of large-scale IoT devices. Therefore, in order to solve this challenge and improve the spectrum efficiency of mMTC, license-free non-orthogonal multiple access (GF-NOMA) was proposed. However, there are still some important issues that need to be resolved. One of them is to design efficient multi-user detection (MUD) schemes to efficiently recover information transmitted from multiple devices simultaneously. In a mMTC network, most devices are usually in a silent state and only a few devices are active. Taking advantage of the natural sparsity of user active status and data transmission, the multi-user detection problem can be regarded as a sparse signal recovery problem under the Compressed Sensing (CS) framework and solved using the Compressed Sensing reconstruction algorithm to improve the GF-NOMA system. performance and efficiency.

Ridge regression detection method (RD), Lasso detection method (LD) and minimum mean square error (MMSE) methods all take the sparsity of the user's active status into account, and they all require known user activity factors, but the first two The performance of the detection method is better than that of the third method. The zero-forcing (ZF) algorithm reduces interference in the system by setting a weight matrix, but it may introduce noise when the condition number of the channel matrix is large. The multi-user detectors of these traditional methods rely on fixed user sparsity and independently recover each sparse signal to solve the multi-user detection problem in a single time slot scenario.

In actual mMTC scenarios, the user's active status is unknown, and the user's active status usually remains unchanged or changes slowly throughout the data frame. Orthogonal matching pursuit (OMP) utilizes limited linear observations to recover sparse signals by iteratively selecting atoms with the largest projections, progressively adding them to the estimated signal and updating the residuals. In this way, the algorithm can gradually approximate the real sparse signal. Multi-user detection based on sparse Bayesian learning (SBL-MUD) treats the multi-user detection problem as a sparse signal recovery problem to achieve better signal recovery and user separation in interference environments. It uses Bayesian learning to estimate which users are transmitting and their signal strength. Within different time slices, SBL can adaptively identify which users are transmitting and restore them while ignoring those who are inactive. However, when user activity status changes in different time slots, the processing effect using the SBL method is not ideal.

Contents of the invention

The purpose of this invention is to provide a sparse Bayesian signal reconstruction method based on multiple measurement vector models, which uses the internal structure of user information to decompose multi-user detection under multi-time slots into multiple single time slots, and then performs each Operate in stages to extract user information to avoid multi-user detection being limited by time slots.

The object of the present invention is achieved through the following technical solution: a sparse Bayesian signal reconstruction method based on multiple measurement vector models, which is characterized in that: in an uplink authorization-free non-orthogonal multiple access system, there are A base station is used to receive data information from K single-antenna users. Assume that the data information of single-antenna users is spread by a spreading code of length N and then sent to the base station. Within L consecutive time slots, only some active users Continuously transmit signals, inactive users do not transmit signals;

Therefore, the signal received by the base station is equivalent to the MMV model. The MMV model refers to the multiple measurement vector model, recorded as:

Y=HB+W,

in, is the channel matrix between the transmitter and the receiver. The channel matrix contains information about the channel response and spreading code;

Transmit signal vector b _l is the transmitted signal of K users in the lth time slot; y _l is the received signal of the base station in the lth time slot;/> w. _l is complex Gaussian noise with zero mean and covariance matrix σ ² Ι, l=1,2,…,L;

When performing sparse Bayesian signal reconstruction, it is necessary to restore the transmitted signal vector B through the known received signal vector Y and channel matrix H, including the following steps:

Step S1: Input the known information, including the received signal, total number of devices, equivalent channel matrix and spreading factor, use automatic decision-making technology (ARD) to assign structured Gaussian prior information to the transmitted signal, and combine the prior information of the noise signal The information is distributed into an ordinary Gaussian distribution, and the set Gaussian distributions of the transmitted signal and noise signal are initialized with hyperparameters to complete the setting of the judgment conditions for successful recovery of the transmitted signal in the entire system;

Step S2: Perform Bayesian calculation on the prior information, solve for the posterior distribution of the transmitted signal, and use the mean value in the posterior distribution as the optimal update rule for the transmitted signal;

Step S3: Under the ARD cost function, combine iterative expectation maximization (EM) to find the estimated values of the hyperparameters in the probability model, and finally obtain the optimal update rules for the emission signal hyperparameters and the noise signal hyperparameters;

Step S4: Determine whether to continue iteration based on the set maximum iteration threshold or the difference between the posterior mean of the two iterations before and after. If the judgment conditions are met, the recovery signal, transmission signal hyperparameters and noise signal hyperparameters are output. If not, return to step S2 starts a new round of iteration.

The beneficial effects of the present invention are:

(1) The present invention assigns structured Gaussian prior information to the transmitted signal, and then uses the Bayesian basic criterion and the expectation maximization algorithm to update the posterior distribution parameters and hyperparameter set of the transmitted signal. This method does not require explicit knowledge of the actual number of active users during the iterative calculation process, thereby increasing calculation flexibility;

(2) The present invention allocates structured Gaussian prior information to the transmitted signal, makes full use of the internal structural characteristics of the transmitted signal, converts multi-time slot problems into single-time slot problems, simplifies the multi-user detection process under multi-time slots, and improves the system performance;

(3) The present invention uses the internal structure of user information to decompose multi-user detection under multi-time slots into multiple single time slots, and then operates each stage to extract user information, thereby solving the problem of multi-user detection under multi-time slots. .

Description of drawings

Figure 1 is a flow chart of a sparse Bayesian signal reconstruction method based on a multiple measurement vector model according to the present invention;

Figure 2 is an analysis diagram of symbol error rates of various multi-user detection methods under Gaussian channels.

Detailed ways

The technical solution of the present invention will be described in further detail below in conjunction with the accompanying drawings, but the protection scope of the present invention is not limited to the following description.

The present invention takes into account that traditional multi-user detection methods require known user activity factors. However, in actual mMTC scenarios, determining the active number of users in a certain time slot is very challenging and difficult to implement. In order to solve this problem, the present invention assigns structured Gaussian prior information to the transmitted signal, and then uses the Bayesian basic criterion and the expectation maximization algorithm to update the posterior distribution parameters and hyperparameter set of the transmitted signal. This method does not require explicit knowledge of the actual number of active users during the iterative calculation process, thereby increasing calculation flexibility;

At the same time, considering that when the channel is complex and the user active status changes within a period of time, the processing effect of using the traditional multi-user detection method is poor, the present invention allocates structured Gaussian prior information to the transmitted signal, making full use of the internal structure of the transmitted signal. Features, convert multi-slot problems into single-slot problems, simplify the multi-user detection process under multi-slots, and improve system performance;

Furthermore, considering that the multi-user detection method using Bayesian theory estimates the prior distribution of the transmitted signal, it can only handle the multi-user detection problem under a single time slot, but cannot handle the multi-user detection problem under multiple time slots. When the signal The result of using this method to process multiple time slots is not ideal. Based on this theory, the present invention makes an improvement, using the internal structure of user information to decompose multi-user detection under multi-time slots into multiple single time slots, and then Each stage is operated to extract user information, which solves the problem of multi-user detection under multi-time slots.

Specifically, in an uplink license-free non-orthogonal multiple access system, there is a base station used to receive data information from K single-antenna users. It is assumed that the data information of the single-antenna users passes through a spreading code of length N. After spreading, it is sent to the base station. Each user transmitting a signal selects the information of L time slots as the transmission information:

Therefore, the signal received by the base station is equivalent to the MMV model. The MMV model refers to the multiple measurement vector model, recorded as:

Y=HB+W,

in, is the channel matrix between the transmitter and the receiver. The channel matrix contains information about the channel response and spreading code;

Among them, the channel response refers to the change of the signal due to the influence of the channel during the propagation process. The channel response is an expression in the time domain, and the channel matrix is an expression in the frequency domain, so part of the channel matrix is the Fourier transform of the channel response, so The channel matrix contains the channel response. Spreading code is a technology that expands the original signal at the transmitter. It is usually used to resist multipath interference and improve anti-interference capabilities. It can be known from the matrix dimension of H that it contains a spreading code of length N, that is, the channel matrix is the product of the channel response and the frequency domain of the spreading code;

Transmit signal vector b _l is the transmitted signal of K users in the lth time slot; y _l is the received signal of the base station in the lth time slot;/> w. _l is complex Gaussian noise with zero mean and covariance matrix σ ² Ι, l=1,2,…,L;

Channels in communication systems are usually assumed to be linear time-invariant systems. This means that the response of the system to the input signal is linear and the properties of the system are invariant in time. In this case, the received signal can be represented as a linear transformation of the transmitted signal through the channel. Noise in communication systems is often modeled as additive white Gaussian noise. This means that noise is an independent and identically distributed Gaussian random variable, and its impact on the signal can be described by its variance.

When performing sparse Bayesian signal reconstruction, the transmitted signal vector B needs to be restored through the known received signal vector Y and channel matrix H;

Referring to Figure 1, a sparse Bayesian signal reconstruction method based on multiple measurement vector models is implemented as follows:

Step S1: Treat b _i· as a sparse signal, so that the signal satisfies a Gaussian distribution with a mean value of 0 and a variance of γ _i I within L time slots, and B represents a combination of K different b _i . B is regarded as a block sparse signal. The prior distribution of B can be expressed as the product of the prior distributions of K _bi· . From this, we can know that B is a Gaussian distribution with a mean of 0 and a covariance of γ. Where γ=(γ ₁ , γ ₂ ,…, γ _K ) ^T , so the Gaussian prior distribution of the transmitted signal B is expressed as,

Among them, p(B; γ) represents the a priori expression that K user signals are controlled by the hyperparameter γ in L time slots, and p(b _i .; γ _i ) represents that one user is controlled by the hyperparameter γ in L time slots. A priori expression of the influence of _i .

In this application, CN(b _i· |0,γ _i I) represents a Gaussian distribution expression. The short vertical line before it represents the parameters that need to be expressed using the Gaussian distribution. The short vertical line after the short vertical line represents the mean and variance of the Gaussian distribution. Use the short vertical line. The vertical line is to more intuitively know which signal this Gaussian distribution represents.

Assume that the noise in the channel is Gaussian white noise, that is, the prior distribution of the noise is a Gaussian distribution with a mean value of 0 and a variance of σ ² I, that is, the prior distribution of the noise is a complex Gaussian distribution p(w _·j )=CN(0 ,σ ² I), the likelihood distribution of the received signal y is expressed as:

p(y _·j |b. _j ) represents the likelihood distribution of K users in the jth time slot, that is, when the transmitted signal is b _·j , the probability of the received signal being y _·j , since the received signal is equal to The linear expression of the channel matrix and the transmitted signal is coupled with noise, and the noise is independently and identically distributed, so the received signal of each time slot can be expressed as a Gaussian distribution with a mean value of Hb _·j and a variance of σ ² I.

Step S2: Based on Bayesian learning theory, calculate the posterior distribution of all user signals in the l-th time slot, and convert the posterior distribution result into a Gaussian distribution pattern to obtain the mean and covariance of the transmitted signal in the l-th time slot:

p(b _·j |y _·j ; γ,σ ² ) represents the posterior distribution of all users in each time slot, where this distribution is affected by the hyperparameters γ and σ ^2. According to Bayes’ theorem, the posterior distribution is equal to The likelihood distribution p(y _·j |b _·h ) of the received signal is multiplied by the prior distribution p(b _·j ;γ) of the transmitted signal. This calculation result uses p(b _·j ,y _·j ;γ,σ ² ) to express it, and then divide it by the marginal distribution p(y _·j ) of the received signal, that is, the full probability. However, the marginal distribution of the received signal is not easy to obtain, so it is expressed by integrating the numerator part of the transmitted signal, and the mean is the exponential part For the zero point of the first derivative of b _·j , the inverse of the covariance matrix is the second derivative of the exponential part with respect to b _·j :

where Г is the K × K diagonal matrix of the hyperparameter γ, μ _·l represents the mean of the l-th time slot, and Cov[.] represents the covariance of the posterior distribution (covariance is used to measure the difference between two random variables Whether the changing trends are consistent, that is, whether they increase or decrease at the same time) M and Σ respectively represent the updated posterior mean and covariance of the transmission signal B, and the updated posterior mean is used as the transmission signal at the next moment.

Step S3: Each unique value of the hyperparameter vector γ corresponds to a different hypothesis of the prior distribution generated by the data Y. Updating the hyperparameter vector is to continuously modify the prior distribution of the signal;

An empirical Bayesian strategy for performing this task is to treat the unknown weight B as a disturbance parameter and integrate it. The resulting margin is then maximized with respect to γ, resulting in an ARD-based cost function:

Among them, -2log(.) is a transformation performed to optimize the calculation process, using marginalization for hyperparameter optimization to compensate for the loss of degrees of freedom associated with the estimated covariance component σ ² and the unknown weight B;

For Bayesian updating of hyperparameters, we focus on marginal likelihood, also known as model evidence. Marginal likelihood is the probability obtained by integrating the model parameters (including hyperparameters) given the observed data. It takes into account all possible parameter values. Marginal likelihood is actually the embodiment of Occam's razor principle. This principle holds that for given observational data, the simpler the model, the better. Marginal likelihood takes into account both how well the model fits the data and the complexity of the model (reflected by the prior distribution of the parameters), so using marginal likelihood as a cost function in hyperparameter optimization helps balance the complexity of the model. and fitting the data.

In order to minimize L(γ,σ ² ), treat B as hidden data and use the EM algorithm to complete this operation. For the E step, use the mean and covariance calculated in step S2 to calculate the posterior moment. For the M step, Choose to perform partial derivatives of γ and σ ² on L(γ, σ ² ) respectively, and set the results to zero to obtain the updated hyperparameter rules:

Step S4: In the present invention, there are two decision methods to check whether the transmission signal is restored successfully, one is that the number of runs reaches R _max , and the other is ‖μ ^(t) -μ ^(t-1) ‖ ₂ ≤ε. If one of the decision conditions is met, the calculated posterior mean value of the last iteration is selected as the recovery signal. If it is not met, step S2 is returned to start a new round of iteration.

In the embodiment of this application, the feasibility of a sparse Bayesian signal reconstruction method based on a multiple measurement vector model is verified through simulation experiments.

Simulation parameters: This invention considers the additive white Gaussian noise (AWGN) channel, the modulation scheme is binary phase shift keying (BPSK), the total number of users is K=20, the user activity factor is p _a =0.3, and the spreading factor is N= 32, the frame structure length is L=6, the maximum number of iterations is R _max =100, the maximum allowable error is ε=10 ^-6 , and the average signal-to-noise ratio (SNR) of active users ranges from 3dB to 20dB.

Simulation results: Figure 2 shows the SER performance analysis chart of each multi-user detection method. It can be seen that the performance of sparse Bayesian detection method is better than traditional detection methods, such as ZF, OMP, MMSE, RD and LD. This is because the sparse Bayesian detection method utilizes the prior information of the emitted signal and is suitable for situations where there are few active users. In addition, the method of the present invention takes into account the internal structural characteristics of each user signal, thereby allocating structured a priori information to the transmitted signal. In this method, each symbol can be restored in multiple time slots, so compared with Compared with the SBL method, this method has superior detection performance.

The above are the specific implementation modes and simulation verification of the present invention. It should be noted that those of ordinary skill in the art can clearly understand that the above embodiments and simulations of the authorization-free joint active user and data detection method of the present invention are only used to illustrate and verify the rationality and feasibility of the method. It is not used to limit the method of the present invention. While the invention has been effectively illustrated and described by way of example, many variations thereof may be made without departing from the spirit of the invention. Without departing from the spirit and essence of the method of the present invention, those skilled in the art can make various corresponding changes or deformations according to the method of the present invention, but these corresponding changes or deformations all fall within the scope of protection required by the method of the present invention. .

Claims (5)

1. A sparse Bayesian signal reconstruction method based on a multiple measurement vector model is characterized by comprising the following steps of: in an uplink unlicensed non-orthogonal multiple access system, a base station is provided, and is used for receiving data information from K single antenna users, and after the data information of the single antenna users is spread by a spreading code with the length of N, selecting information of L time slots as transmitting information and transmitting the transmitting information to the base station; in L continuous time slots, only part of active users continuously transmit signals, and inactive users do not transmit signals;

from this, the base station received signal is equivalent to an MMV model, which refers to a multiple measurement vector model, and is noted as:

Y＝HB+W，

wherein,is a channel matrix between a transmitting end and a receiving end, wherein the channel matrix contains information of channel response and spread spectrum codes; transmit signal vector->b _l Is the transmission signal of the K users of the first time slot;y _l is the received signal of the first time slot base station; />w. _l Is zero mean and sigma covariance matrix ² Complex gaussian noise of i, l=1, 2, …, L; when the sparse Bayesian signal reconstruction is carried out, a transmitting signal vector B needs to be recovered through a known receiving signal vector Y and a channel matrix H;

the sparse Bayesian signal reconstruction method comprises the following steps:

step S1: inputting known information, including received signals, total number of devices, equivalent channel matrix and spread spectrum factor, using automatic decision technique to distribute structured Gaussian prior information to the transmitted signals, distributing prior information of noise signals into common Gaussian distribution, and carrying out super-parameter initialization on the set Gaussian distribution of the transmitted signals and the noise signals;

step S2: combining the prior information with the Bayesian theorem to obtain posterior distribution results of the transmitting signals, combining the posterior results obtained by calculation into a Gaussian mode, and selecting posterior mean values of the transmitting signals as updated values of the transmitting signals;

step S3: under the ARD cost function, calculating to obtain an estimated value of the super parameter in the probability model by combining with an iteration expectation maximization framework, and obtaining an optimal updating rule of the super parameter in the transmitting signal and the super parameter in the noise signal;

step S4: judging whether iteration is continued or not according to the set judgment conditions, if the judgment conditions are met, outputting the recovered transmitting signals, the transmitting signal super-parameters and the noise signal super-parameters, and if the judgment conditions are not met, returning to the step S2 to perform a new iteration.

2. The sparse bayesian signal reconstruction method based on the multiple measurement vector model according to claim 1, wherein: the step S1 includes:

s101, input baseStation receiving signal Y and equivalent channel matrix H, setting maximum circulation times R _max And a maximum allowable error epsilon;

s102, b _i Consider a sparse signal that satisfies a mean of 0 and a variance of γ in L time slots _i Gaussian distribution of I, and B represents K different B _i Combining, regarding B as a block sparse signal, the a priori distribution of B is expressed as K B _i The product of the a priori distributions can be found that B is a gaussian distribution satisfying a mean of 0 and a covariance of γ, where γ= (γ) ₁ ,γ ₂ ,…,γ _K ) ^T The gaussian a priori distribution of the transmitted signal B is expressed as,

where p (B; gamma) represents a priori the expression of K user signals in L time slots under the control of the super parameter gamma, p (B) _i .；γ _i ) Indicating that a user is subject to super parameter gamma in L time slots _i A priori expression of the effect; CN (b) _i .|0,γ _i I) In the middle, parameters which need to be expressed by using Gaussian distribution are represented in front of a short vertical line, and the mean value and the variance of the Gaussian distribution are represented in back of the short vertical line;

s103, setting noise in the channel as Gaussian white noise, namely the prior distribution of the noise is 0 as the mean value and sigma as the variance ² The gaussian distribution of I, i.e. the a priori distribution of noise, is a complex gaussian distribution p (w). _j )＝CN(0,σ ² I) The likelihood distribution of the received signal y is expressed as:

p(y _.j |b _.j ) Representing likelihood distribution of K users in the jth time slot, i.e. when the transmitted signal is b _.j In the case of (2), the received signal is y _.j Since the received signal is equal to the linear representation of the channel matrix and the transmitted signal plus noise, and the noise is independentAre distributed so that the received signal for each slot is represented as Hb in average _.j Variance is sigma ² A gaussian distribution of I.

3. The sparse bayesian signal reconstruction method based on the multiple measurement vector model according to claim 1, wherein: the step S2 includes:

based on Bayesian learning theory, calculating posterior distribution of all user signals in the first time slot, and converting posterior distribution results into a Gaussian distribution mode to obtain mean and covariance of the transmitted signals in the first time slot:

wherein p (b). _j |y. _j ；γ,σ ² ) Representing the posterior distribution of all users per slot, where this distribution is subject to the super parameters gamma and sigma ² Is a function of (1);

where r is the K x K diagonal matrix of the super parameter γ, μ. _l Represents the mean value of the first slot, cov [.]The covariance of the posterior distribution is calculated, M and sigma respectively represent the posterior mean value and covariance updated by the transmitted signal B, and the posterior mean value after updating is taken as the transmitted signal at the next moment.

4. The sparse bayesian signal reconstruction method based on the multiple measurement vector model according to claim 1, wherein: the step S3 includes:

each unique value of the super-parameter vector gamma corresponds to different assumptions of the prior distribution generated by the data Y, and the super-parameter vector is updated, namely the prior distribution of the transmission signal is continuously modified;

the empirical bayesian strategy to perform this task is to consider the unknown weight B as an interference parameter and integrate it, and then maximize the marginal of the result relative to γ, yielding an ARD-based cost function:

wherein, -2log () is a transformation performed to optimize the computation process, and wherein marginalization is used to perform superparameter optimization, compensation and estimation of covariance component σ ² And degree of freedom loss associated with the unknown weight B;

to minimize L (gamma, sigma) ² ) Regarding B as hidden data, using EM algorithm to accomplish this, for E step, using the mean and covariance calculated in step S2 to calculate a posterior moment, for M step, selecting a pair L (gamma, sigma) ² ) Gamma and sigma are performed respectively ² And setting the results to zero to obtain updated hyper-parameter rules:

5. the sparse bayesian signal reconstruction method based on the multiple measurement vector model according to claim 1, wherein: in the step S4, when the running number reaches the maximum cycle number t=r _max Or when the two norms of the difference value between the posterior mean value obtained in the iteration of the round and the posterior mean value of the previous round are smaller than the maximum allowable error epsilon set in the step S1, ending the cyclic operation, and taking the posterior mean value of the B calculated in the last round as a recoveryA complex transmit signal; if the iteration termination condition is not satisfied, let t=t+1, and return to step S2 for the next iteration based on the super parameter set updated in step S3.